By Makoto Nakajima
The author introduces risk-averse preferences, labor-leisure choice, capital, individual productivity shocks, and market incompleteness to the standard Mortensen-Pissarides model of search and matching and explore the model’s cyclical properties. There are four main findings. First and foremost, the baseline model can generate the observed large volatility of unemployment and vacancies with a realistic replacement ratio of the unemployment insurance benefits of 64 percent. Second, labor-leisure choice plays a crucial role in generating the large volatilities; additional utility from leisure when unemployed makes the value of unemployment close to the value of employment, which is crucial in generating a strong amplification, even with the moderate replacement ratio. Besides, it contributes to the amplification through an adjustment in the intensive margin of labor supply. Third, the borrowing constraint or uninsured individual productivity shocks do not significantly affect the cyclical properties of unemployment and vacancies: Most workers are well insured only with self-insurance. Fourth, the model better replicates the business cycle properties of the U.S. economy, thanks to the co-existence of adjustments in the intensive and extensive margins of labor supply and the stronger amplification.
This paper is a technical tour de force as it combines a search model with a real business cycle model, aggregate and idiosyncratic shocks, incomplete markets and thus heterogeneity, intensive and extensive labor margins. All that is missing is the external sector… But beyond the technical achievement, this paper addresses important questions. It resolves the Shimer with a much lower unemployment benefit than previous papers (although still somewhat high compared to data, so there is still room for improvement). It turns out self-insurance is not critical, but leisure is. And the model is good at replicating US business cycles.